Peter Kleinschmidt constructs (up to isomorphism) all smooth normal toric varieties with dimension
rays; see P. Kleinschmidt, A classification of toric varieties with few generators,
(1998) 254-266.
, we obtain a variety isomorphic to a Hirzebruch surface.
i1 : X = kleinschmidt(2,{3});
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i2 : rays X
o2 = {{-1, 0}, {1, 0}, {0, 1}, {3, -1}}
o2 : List
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i3 : max X
o3 = {{0, 2}, {0, 3}, {1, 2}, {1, 3}}
o3 : List
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i4 : FF3 = hirzebruchSurface 3;
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i5 : rays FF3
o5 = {{1, 0}, {0, 1}, {-1, 3}, {0, -1}}
o5 : List
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i6 : max FF3
o6 = {{0, 1}, {0, 3}, {1, 2}, {2, 3}}
o6 : List
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< d-r+1.